We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.
A spectral expansion for the symmetric space $\mathrm{GL}_n(E)/\mathrm{GL}_n(F)$
A characteristic map for the symmetric space of symplectic forms over a finite field
Approximation of $L^2$-analytic torsion for arithmetic quotients of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$
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